A decoupled flexible‐relative co‐ordinate recursive approach for flexible multibody dynamics

Abstract

AbstractAn extended kinematic graph concept and a variational‐vector calculus approach are employed to develop a new recursive formulation for the dynamic analysis of flexible multibody systems. The extended graph concept introduced defines frames and transformations between frames as nodes and edges, respectively, rather than the more traditional body and joint convention. Kinematic relationships between adjacent flexible bodies are derived, using joint relative co‐ordinates and a state vector notation that represents both translational and rotational components of velocity. Deformation kinematics are formulated in terms of modal co‐ordinates, under small deformation assumptions. Joint relative co‐ordinates are decoupled from deformation modal co‐ordinates in both kinematic relations and in the recursive dynamics algorithm, leading to a significant reduction in the dimension of matrices that must be inverted. Dynamic analysis of a flexible closed‐loop spatial robot is performed to illustrate the efficiency of the algorithm.